This article mainly focused on high level Density Functional Theory (DFT) studies on the chiral phosphoric acid-catalyzed Friedel-Crafts reactions between 4,7-dihydroindoles and nitroolefins. Firstly, the reactivities of 4,7-dihydroindole and indole in the chiral phosphoric acid-catalyzed Friedel-Crafts reactions with nitroolefin have been compared. The higher reactivity of 4,7-dihydroindole could be attributed to its higher HOMO energy as well as its more suitable trajectory to attack the nitroolefin in the transition state. Secondly, the origin of the enantioselectivity of the chiral phosphoric acid-catalyzed Friedel-Crafts reaction of 4,7-dihydroindole with nitroolefin has been studied using complete models on PBE1PBE/[6-311+G(d,p), 6-31G(d,p)] level. When (S)-1b was used as the catalyst, the enantioselectivity of the reaction is entirely controlled by the steric effect between the catalyst and the substrate. Whereas for catalyst (S)-1c the enantioselectivity is determined by the solvent effect. (C) 2010 Elsevier Ltd. All rights reserved.